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The equation of motion for the Skyrme model with a pion mass term is studied in the framework of the Painleve analysis, and information is obtained about the singularity structure of its solutions. As in the massless case, singularities exist, consisting of a first‐order pole term superposed to a logarithmic branch point. For the solitonic solutions, the singularities form an infinite sequence of points located on the negative real axis of the squared radial variable, accumulating at the origin. Based on this property and on the asymptotic behavior of the solitonic solutions, an approximate representation is built for the baryonic soliton, which is extremely accurate. more...

The singularity structure of the solutions of the equations of motion for the Sigma and Skyrme model Lagrangians with the hedgehog ansatz is investigated. In both cases the solutions present superposed a polelike term and a logarithmic branch point. The set of solitonic configurations of the Skyrme model is characterized by the sequence of locations of their singularities on the negative real axis of the dimensionless variable z = (eFπr)2, with an accumulation point at z=0. The first few terms of the Laurent series representing the Skyrme soliton profile are shown to reproduce well the exact values in an interval about the origin. Pade approximants to the residual power series obtained after subtraction of the dominant pole term are modified in order to satisfy the constraints imposed by the asymptotic power series expansion, and approximate representations are built for the Skyrme soliton configuration, which are shown to combine simplicity with accuracy. more...

All kinds of solution of the Euler–Lagrange equation obtained from the chiral nonlinear sigma model Lagrangian with the hedgehog ansatz for the SU(2) field are investigated. Making use of the scale invariance of the equation of motion, the solutions are classified in families, according to their analytic properties. It will be shown that the energy integral diverges for all possible classes of solution, and that a finite topological charge can be defined for only one class of solution, and has only one possible numerical value (and its negative). more...

Properties of the Euler–Lagrange differential equation for cos F, where F is the chiral angle of the classical Skyrme soliton in the hedgehog ansatz, are investigated. The power series solution for y=cos F, is obtained that presents the behavior of an almost geometric series, and the existence of single poles located at imaginary values of the radial variable r is shown. Pade approximants are built to the series expansion about the origin, and its terms are modified in order to incorporate the main features of the asymptotic behavior of the field configuration. Thus rational fractions are constructed which provide very good and practical analytical representations of the Skyrme soliton profile function. more...

The representation of the usual integral dispersion relations (IDR) of scattering theory through series of derivatives of the amplitudes is discussed, extended, simplified, and confirmed as mathematical identities. Forms of derivative dispersion relations (DDR) valid for the whole energy interval, recently obtained and presented as double infinite series, are simplified through the use of new sum rules of the incomplete $\Gamma$ functions, being reduced to single summations, where the usual convergence criteria are easily applied. For the forms of the imaginary amplitude used in phenomenology of hadronic scattering, we show that expressions for the DDR can represent, with absolute accuracy, the IDR of scattering theory, as true mathematical identities. Besides the fact that the algebraic manipulation can be easily understood, numerical examples show the accuracy of these representations up to the maximum available machine precision. As consequence of our work, it is concluded that the standard simplified forms sDDR, originally intended for the high energy limits, are an inconvenient and incomplete separation of terms of the full expression, leading to wrong evaluations. Since the correspondence between IDR and the DDR expansions is linear, our results have wide applicability, covering more general functions, built as combinations of well studied basic forms., Comment: 27 pages, 5 figures Few changes in text and in references To be published in Journal of Mathematical Physics more...

Properties of the solutions of the Schrodinger equation with a velocity‐dependent potential are studied. Particular attention is given to the examination of the singularities of the differential equation. In the particular cases of one dimension and of the l = 0 partial wave of a spherically symmetric problem, a simple correspondence is found between the velocity‐dependent problem and a static one. more...

Solutions of the Schrodinger equation with a velocity‐dependent potential are discussed. The analytic behavior of the S matrix as a function of the momentum is investigated, and some properties of general validity are demonstrated. The configuration of the poles of the scattering matrix in the complex‐momentum plane is described in detail for the case of a spherically symmetric potential. more...